78 ACOUSTICAL ELEMENTS 



5.3. Acoustic Impedance of a Tube of Small Diameter. — The trans- 

 mission of sound waves or direct currents of air in a small tube is influenced 

 by resistance due to viscosity. The diameter is assumed to be small com- 

 pared to the length so that the end correction may be neglected. The 

 length is assumed to be small compared to the wavelength. The diameter 

 is assumed to be small compared to the length. 



The acoustic impedance of a small diameter tube ^'^'^ is given by 



Za = 



/ /8m 4 . \ 



where R = radius of the tube, in centimeters, 



^x = viscosity coefficient, 1.86 X 10~^ for air 

 60 = It/, f = frequency, in cycles per second, 

 / = length of the tube, in centimeters, and 

 p = density, in grams per cubic centimeter. 

 The effect of viscosity is to introduce resistance in the form of dissipa- 

 tion as well as to add to the reactance. 



The resistance of a single hole is ordinarily much too high. The desired 

 resistance may be obtained by using a sufficient number of holes. 



Silk cloth provides a simple means of obtaining acoustic resistance of 

 this type. It has been used in microphones and telephone receivers for 

 many years. The ratio of the resistance to the reactance is governed by 

 the size of the holes. The amount of resistance may be controlled by the 

 number of layers and the area. 



5.4. Acoustic Impedance of a Narrow Slit. — A narrow slit acts in a 

 manner quite similar to the narrow tube. The length is assumed to be 

 small compared to the wavelength. The thickness is assumed to be small 

 compared to the length. 



The acoustic impedance of a narrow slit ^-^-^ is given by 



1 2iJiW . 6pwoi 



where ju = viscosity coefficient, 1.86 X 10"^ for air, 

 p = density, in grams per cubic centimeter, 



^ Crandall, " Vibrating Systems and Sound," D. Van Nostrand Co., New York. 



^ Lamb, " Dynamical Theory of Sound," E. Arnold, London. 



•* Rayleigh, " Theory of Sound," Macmillan and Co., London. 



'' Crandall, " Vibrating Systems and Sound," D. Van Nostrand Co., New York. 



^ Lamb, " Dynamical Theory of Sound," E. Arnold, London. 



" Rayleigh, " Theory of Sound," Macmillan and Co., London. 



